Determining resistivity anistotropy and formation structure for vertical wellbore sections

ABSTRACT

Formation properties in a vertical section of a wellbore are determined by considering the vertical section as consisting of one or more segments. Measurements are obtained with a directional resistivity tool at two or more measurement stations within each segment for which the complex 0 th  harmonic coefficients for the obtained measurements are non-trivially different from one another. For each such segment, the phase shift and attenuation are determined using the complex 0 th  harmonic coefficients obtained for that segment and an inversion is performed for the formation properties using the determined phase shift and attenuation for that segment. Formation properties for that segment may be output to a display or memory storage device. For certain segments, one or more gain factors may be obtained. The gain factors are used to correct the measured voltages for certain neighboring segments and the corrected voltages inverted to obtain anisotropy and formation structure.

CROSS-REFERENCE TO OTHER APPLICATIONS

This application claims priority to and the benefit of U.S. ProvisionalApplication Serial Number 61/357,164, filed on Jun. 22, 2010.

BACKGROUND

1. Technical Field

This disclosure relates generally to oil and gas well logging, and morespecifically, to directional resistivity measurements. Still morespecifically, two embodiments of a method are disclosed for determiningresistivity anisotropy and formation structure from deep resistivitymeasurements in vertical wellbore sections. Other measurements aredisclosed as well.

2. Description of the Related Art

An alternative to wireline logging techniques is the collection of dataon downhole conditions during the drilling process. By collecting andprocessing such information during the drilling process, the driller canmodify or correct key steps of the operation to optimize performance.Schemes for collecting data of downhole conditions and movement of thedrilling assembly during the drilling operation are known asmeasurement-while-drilling (“MWD”). Similar techniques focusing more onmeasurement of formation parameters than on movement of the drillingassembly are known as logging-while-drilling (“LWD”). However, the termsMWD and LWD are often used interchangeably, and the use of either termin this disclosure will be understood to include both the collection offormation and wellbore information, as well as data on movement andplacement of the drilling assembly.

Measurement-while-drilling (MWD) tools are available to guide drillstrings and therefore the resulting wellbores into more productivereservoir zones. MWD tools used for this purpose typically have beenpropagation resistivity tools, also known as array compensatedresistivity (ARC) tools, with a 360° measurement and deep imagingcapability to detect fluid contacts and formation changes up to 15 feetfrom the wellbore. Measurements are commonly made of the phase-shift andattenuation of the signals at the receiver coils, which are indicativeof the formation conductivity.

Currently available ARC tools are non-azimuthal and use two receivers tocompensate for any electronic drift associated with the transmitter. Theelectronic drift associated with the two receivers and any imbalancebetween the two receivers is removed using a scheme called boreholecompensation, which involves the use of a second transmittersymmetrically placed with respect to the first transmitter. Thetransmitters are alternately energized so two phase shifted signals canbe measured when the two transmitter coils operate at identicalfrequencies. However, using two transmitter coils alternately slows therate of data acquisition, which can lead to errors due to the time delaybetween sequential measurements. Further, use of multiple transmittersmay require the signals to be time-multiplexed when operating at thesame frequency to avoid cross-talk. Multiplexing slows the rate of dataacquisition. The errors due to time delays are magnified when drillingrates are high.

Another problem associated with conventional propagation resistivity orARC tools is that the magnetic dipole moments of the transmitters andreceivers are oriented axially with respect to the tool axis. Suchmeasurements are only sensitive to or affected by the anisotropy whenthe relative dip angle (θ) is greater than 45° . Further, in homogeneousformations, vertical resistivity and relative dip angle are coupled. Asa result, even with a relative high dip angle, simultaneousdetermination of horizontal resistivity (R_(h)), vertical resistivity(R_(v)), and the relative dip angle (θ) is not possible for homogeneousformations. Environmental effects may break the coupling between R_(h)and θ, but that is uncertain and variable from formation to formation.

As an improvement over propagation resistivity or ARC tools,Schlumberger developed the PERISCOPE™ 15 deep imaging LWD tool, whichincorporates tilted and transverse antennas in the drilling collar. Thenon-axial antennae obtain directional electromagnetic measurements. Onecan define the attenuation ATT as a logarithmic function of the ratiobetween two different linear combinations of the electromagneticcoupling tensor coefficients V_(xx), V_(yy), and V_(zx):

$\begin{matrix}{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{V_{xx} + V_{yy} + V_{xz}}{V_{xx} + V_{yy} - V_{xz}} \right)} \right)}}} & \left( {1a} \right)\end{matrix}$

and the phase shift PS as the difference between two arctangentfunctions, using real and imaginary components of the electromagneticcoupling tensor components, at the same wellbore station:

$\begin{matrix}{{PS} = {{a\; {\tan \left( \frac{V_{xx}^{i} + V_{yy}^{i} - V_{xz}^{i}}{V_{xx}^{r} + V_{yy}^{r} - V_{xz}^{r}} \right)}} - {a\; {{\tan \left( \frac{V_{xx}^{i} + V_{yy}^{i} + V_{xz}^{i}}{V_{xx}^{r} + V_{yy}^{r} + V_{xz}^{r}} \right)}.}}}} & \left( {1b} \right)\end{matrix}$

These directional measurements, for which the electronic drifts of boththe transmitter and receiver are removed (or gain corrected), are usedto determine the distance to and azimuthal orientation of formationboundaries in any type of mud. These measurements are typicallytransmitted uphole and displayed on a graphical interface to provideinformation on distance to boundaries, formation resistivity, andorientation. These measurements are sensitive to resistivity anisotropyeven at very low relative angles (e.g., 10°), which is critical in lowresistivity pay zones and in laminated formations because accurateidentification and characterization of hydrocarbon reserves is notpossible without knowing the resistivity anisotropy.

Unfortunately, the azimuthal sensitivity of a non-axialtransmitter/receiver pair disappears in a perfectly vertical sectionwith 0° relative dip angle θ. In other words, the 1^(st) and the 2^(nd)harmonic coefficients (i.e., C_(1c), C_(1s), C_(2c), and C_(2s)), whichcontribute to the azimuthal sensitivity (as seen from Equation 2 below),vanish as the dip angle θ approaches zero:

V({right arrow over (r)}, φ)=C ₀({right arrow over (r)})+C _(1c)({rightarrow over (r)})cos(φ)+C _(1s)({right arrow over (r)})sin(φ)+C_(2c)({right arrow over (r)})cos(2φ)+C _(2s)({right arrow over (r)})sin2φ)  (2)

As a result, the directional measurements defined in Equations 1a and 1bare zero, therefore improved methods for inverting tool data forresistivity anisotropy and dip angle θ for vertical wellbore sectionsare needed.

SUMMARY OF THE DISCLOSURE

In satisfaction of the aforenoted needs, embodiments of a new method aredisclosed for inverting resistivity data for resistivity anisotropy andformation structure information such as relative dip angle for verticalwellbore sections. In the disclosed method, resistivity anisotropyand/or formation structure can be determined from measurements taken invertical wellbore sections.

Formation properties in a vertical section of a wellbore are determinedby considering the vertical section as consisting of one or moresegments. Measurements are obtained with a directional resistivity toolat two or more measurement stations within each segment for which thecomplex 0^(th) harmonic coefficients for the obtained measurements arenon-trivially different from one another. For each such segment, thephase shift and attenuation are determined using the complex 0^(th)harmonic coefficients obtained for that segment and an inversion isperformed for the formation properties using the determined phase shiftand attenuation for that segment. Formation properties for that segmentmay be output to a display or memory storage device.

For certain segments, one or more gain factors may be obtained. The gainfactors are used to correct the measured voltages for certainneighboring segments and the corrected voltages inverted to obtainanisotropy and formation structure.

To reiterate, in one embodiment, one step comprises identifying a firstsegment of a wellbore and a second segment of the wellbore. One or moregain factors for the second section are calculated and assumed to applyto the nearby first segment. Alternatively, in another embodiment, asegment within a vertical section is identified where the complex 0^(th)harmonic coefficient varies from measurement station to measurementstation. One or more gain factors for that particular segment arecalculated and assumed to apply to the rest of the vertical section.Therefore, for N measurement stations with N complex 0^(th) harmoniccoefficients C₀({right arrow over (r)}₁), . . . C₀({right arrow over(r)}_(N)) within the identified segment of the vertical section, themethod comprises calculating an attenuation value ATT and a phase shiftvalue PS based on Equations 3a and 3b, or 3c and 3d, respectively:

$\begin{matrix}{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{{V_{xx}\left( {\overset{->}{r}}_{i} \right)} + {V_{yy}\left( {\overset{->}{r}}_{i} \right)}}{{V_{xx}\left( {\overset{->}{r}}_{j} \right)} + {V_{yy}\left( {\overset{->}{r}}_{j} \right)}} \right)} \right)}}} & \left( {3a} \right) \\{{PS} = {{a\; {\tan \left( \frac{V_{xx}^{i} + \left( {\overset{->}{r}}_{j} \right) + {V_{yy}^{i}\left( {\overset{->}{r}}_{j} \right)}}{{V_{xx}^{r}\left( {\overset{->}{r}}_{j} \right)} + {V_{yy}^{r}\left( {\overset{->}{r}}_{j} \right)}} \right)}} - {a\; {\tan \left( \frac{{V_{xx}^{i}\left( {\overset{->}{r}}_{i} \right)} + {V_{yy}^{i}\left( {\overset{->}{r}}_{i} \right)}}{{V_{xx}^{r}\left( {\overset{->}{r}}_{i} \right)} + {V_{yy}^{r}\left( {\overset{->}{r}}_{i} \right)}} \right)}}}} & \left( {3b} \right) \\{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{C_{0}\left( {\overset{->}{r}}_{i} \right)}{C_{0}\left( {\overset{->}{r}}_{j} \right)} \right)} \right)}}} & \left( {3c} \right) \\{{PS} = {{a\; {\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{j} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{j} \right)} \right)}} - {a\; {{\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{i} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{i} \right)} \right)}.}}}} & \left( {3d} \right)\end{matrix}$

The superscripts i and r refer to real and imaginary parts,respectively, and the subscripts i and j refer to two different toollocations or measurement stations, respectively. The “atan” means thearctangent. Using the results from Equations 3a and 3b (or 3c and 3d),with or without other measurements, resistivity anisotropy and formationstructure can be calculated for the vertical wellbore section.

Other advantages and features will be apparent from the followingdetailed description when read in conjunction with the attacheddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the disclosed methods andapparatuses, reference should be made to the embodiment illustrated ingreater detail on the accompanying drawings, wherein:

FIG. 1 illustrates, partially in schematic and block form, a wellsitesystem that can be used for formation evaluation, in accordance with thepresent disclosure; and

FIG. 2 is a partial schematic view of a deep imaging resistivity toolthat can be used for formation evaluation, in accordance with thepresent disclosure.

FIG. 3 is a flowchart showing the steps of one embodiment, in accordancewith the present disclosure.

FIG. 4 is a flowchart showing the steps of an alternative embodiment, inaccordance with the present disclosure.

It should be understood that the drawings are not to scale and that thedisclosed embodiments are sometimes illustrated diagrammatically and inpartial views. In certain instances, details that are not necessary foran understanding of the disclosed method and apparatus or that wouldrender other details difficult to perceive may have been omitted. Itshould be understood that this disclosure is not limited to theparticular embodiments illustrated herein.

DETAILED DESCRIPTION

FIG. 1 illustrates a wellsite system. The wellsite can be onshore oroffshore. In this exemplary system, a wellbore 11 is formed insubsurface formations by rotary drilling in a manner that is well known.Directional drilling can also be performed.

A drill string 12 is suspended within wellbore 11 and has a bottom holeassembly (BHA) 100 that includes a drill bit 105 at its lower end. Thesurface system includes platform and derrick assembly 10 positioned overthe wellbore 11 and the assembly 10 includes a rotary table 16, kelly17, hook 18, and rotary swivel 19. The drill string 12 is rotated by therotary table 16, energized by means not shown, that engages the kelly 17at the upper end of the drill string 12. The drill string 12 issuspended from hook 18, attached to a traveling block (also not shown),and the rotary swivel 19 permits rotation of the drill string 12relative to the hook. As is well known, a top drive system couldalternatively be used.

The surface system of FIG. 1 further includes drilling fluid or mud 26stored in a pit 27 formed at the wellbore site. A pump 29 delivers thedrilling fluid 26 to the interior of the drill string 12 via a port inthe swivel 19, causing the drilling fluid 26 to flow downwardly throughthe drill string 12 as indicated by the directional arrow 8. Thedrilling fluid 26 exits the drill string 12 via ports in the drill bit105, and then circulates upwardly through the annular region between theoutside of the drill string 12 and the wall 13 of the wellbore 11, asindicated by the directional arrows 9. In this known manner, thedrilling fluid 26 lubricates the drill bit 105 and carries formationcuttings up to the surface. The cuttings are typically removed from thedrilling fluid 26 before it is returned to the pit 27 for recirculation.

The bottom hole assembly 100 includes a logging-while-drilling (LWD)module 120, a measuring-while-drilling (MWD) module 130, aroto-steerable system and motor 150, and drill bit 105. The LWD module120 is housed in a special type of drill collar, as is known in the art,and can contain one or a plurality of known types of logging tools. Itwill also be understood that more than one LWD and/or MWD module can beemployed, e.g., as represented at 120A. References, throughout, to amodule at the position of 120 can alternatively mean a module at theposition of 120A as well. The LWD module 120 includes capabilities formeasuring, processing, and storing information, as well as forcommunicating with the surface equipment. The LWD module 120 mayinclude, for example, a directional resistivity measuring device.

The MWD module 130 is also housed in a type of drill collar, as is knownin the art, and can contain one or more devices for measuringcharacteristics of the drill string and drill bit. The MWD tool 130further includes an apparatus (not shown) for generating electricalpower to the downhole system, such as a mud turbine generator powered bythe flow of the drilling fluid. Other power and/or battery systems maybe employed. The MWD module 130 may include one or more of the followingtypes of measuring devices: a weight-on-bit measuring device, a torquemeasuring device, a vibration measuring device, a shock measuringdevice, a stick-slip measuring device, a direction measuring device, andan inclination measuring device.

In the system of FIG. 1, a drill string telemetry system is employedthat, in the illustrated embodiment, comprises a system of inductivelycoupled wired drill pipes 180 that extend from a surface sub 185 to aninterface sub 110 in the bottom hole assembly 100. Depending on factorsincluding the length of the drill string, relay subs or repeaters 182can be provided at intervals in the string of wired drill pipes 180. Theinterface sub 110 provides an interface between the communicationscircuitry of the LWD and MWD modules 120, 130 and the drill stringtelemetry system that, in this embodiment, comprises inductively coupledwired drill pipes 180. The wired drill pipes 180 can be coupled with anelectronics subsystem 30 that rotates with kelly 17 and includes atransceiver and antenna that communicate bi-directionally with antennaand transceiver of logging and control unit 4, which includes an upholeprocessor subsystem. In FIG. 1, a communication link 175 isschematically depicted between the electronics subsystem 30 and antenna5 of the logging and control unit 4. Accordingly, the configuration ofFIG. 1 provides a communication link from the logging and control unit 4through communication link 175, to surface sub 185, through the wireddrill pipe telemetry system, to downhole interface 110 and thecomponents of the bottom hole assembly 110 and, also, the reversethereof, for bi-directional operation.

While only one logging and control unit 4 at one wellsite is shown, oneor more surface units across one or more wellsites may be provided. Thesurface units may be linked to one or more surface interfaces using awired or wireless connection via one or more communication lines. Thecommunication topology between the surface interface and the surfacesystem can be point-to-point, point-to-multipoint ormultipoint-to-point. The wired connection includes the use of any typeof cables or wires using any type of protocols (serial, Ethernet, etc.)and optical fibers. The wireless technology can be any kind of standardwireless communication technology, such as IEEE 802.11 specification,Bluetooth, zigbee or any non-standard RF or optical communicationtechnology using any kind of modulation scheme, such as FM, AM, PM, FSK,QAM, DMT, OFDM, etc. in combination with any kind of data multiplexingtechnologies such as TDMA, FDMA, CDMA, etc.

FIG. 2 is a simplified schematic view of a directional deep-readinglogging-while-drilling tool 121, as part of the LWD tool or tools 120 inFIG. 1. Signals from tools having axially aligned cylindricallysymmetrical coils are not directionally sensitive. The tool 121 of FIG.2 includes five axially aligned transmitters T1-T5, a transversetransmitter T6 and two tilted receivers R3, R4 for obtainingdirectionally sensitive measurements and compensated phase shift andattenuation values. Transmitter T4 and receiver R3 can be used for adirectional measurement, or combined with the directional measurementfrom another pair such as T5/R4 to form a symmetrized oranti-symmetrized measurement.

The method disclosed herein allows for the determining of resistivityanisotropy and formation structure information for a vertical formationsection. A voltage at a receiver R4 induced by an electromagnetic fieldtransmitted from a transmitter T6 is given by Equation 2 above (repeatedhere):

V({right arrow over (r)}, φ)=C ₀({right arrow over (r)})+C _(1c)({rightarrow over (r)})cos(φ)+C _(1s)({right arrow over (r)})sin(φ)+C_(2c)({right arrow over (r)})cos(2φ)+C _(2s)({right arrow over (r)})sin2φ)

wherein {right arrow over (r)} is a measurement reference position and θis the azimuth angle of the receiver. Complex coefficientsC₀,C_(1c),C_(1s), C_(2c) and C_(2s), defined below, represent thecomplex 0^(th), 1^(st), and 2^(nd) harmonic coefficients of the voltage:

$\begin{matrix}{{{{C_{0}\left( \overset{->}{r} \right)} = {\frac{1}{2}\left( {{V_{xx}\left( \overset{->}{r} \right)} + {V_{yy}\left( \overset{->}{r} \right)}} \right){\sin \left( \theta_{R} \right)}{\sin \left( \theta_{T} \right)}{\cos \left( \varphi_{T} \right)}}};}{{{C_{1\; c}\left( \overset{->}{r} \right)} = {{V_{zx}\left( \overset{->}{r} \right)}{\cos \left( \theta_{R} \right)}{\sin \left( \theta_{T} \right)}{\cos \left( {\varphi_{B} - \varphi_{T}} \right)}}};}{{{C_{1\; s}\left( \overset{->}{r} \right)} = {{V_{zx}\left( \overset{->}{r} \right)}{\cos \left( \theta_{R} \right)}{\sin \left( \theta_{T} \right)}{\sin \left( {\varphi_{B} - \varphi_{T}} \right)}}};}{{{C_{2\; c}\left( \overset{->}{r} \right)} = {\frac{1}{2}\left( {{V_{xx}\left( \overset{->}{r} \right)} - {V_{yy}\left( \overset{->}{r} \right)}} \right){\sin \left( \theta_{R} \right)}{\sin \left( \theta_{T} \right)}{\cos \left( {{2\varphi_{B}} - \varphi_{T}} \right)}}};}{{{C_{2s}\left( \overset{->}{r} \right)} = {\frac{1}{2}\left( {{V_{xx}\left( \overset{->}{r} \right)} - {V_{yy}\left( \overset{->}{r} \right)}} \right){\sin \left( \theta_{R} \right)}{\sin \left( \theta_{T} \right)}{\sin \left( {{2\varphi_{B}} - \varphi_{T}} \right)}}};}} & (4)\end{matrix}$

where θ_(R) and θ_(T) are the receiver and transmitter angles,respectively, with respect to the tool axis 153, φ_(T) is the azimuthangle of the transmitter relative to the receiver, and φ_(B) is theazimuthal angle of the bed boundary.

Because only three electromagnetic coupling components, V_(xx), V_(yy),and V_(zx), are involved in the expressions for the complexcoefficients, their analytic solutions, apart from a gain factor, andthe solution for the bed boundary angle φ_(B), can be obtained easily.Further, a number of measurements can be based on a logarithmic ratio ofdifferent linear combinations of V_(xx), V_(yy), and V_(zx). While thesemeasurements are sensitive to resistivity anisotropy and relative dipangle θ, they are zero in a vertical wellbore section, as explainedabove. The disclosed method and refinements thereof, as described below,circumvent the problem of measurements that use linear combinations ofV_(xx), V_(yy), and V_(zx) when those components are zero in verticalwellbore sections.

Instead of defining the measurement based on the logarithmic ratio ofdifferent linear combinations of V_(xx), V_(yy), and V_(zx) measured atthe same tool location {right arrow over (r)}, a new measurement isbased on the logarithmic ratio of a linear combination of V_(xx),V_(yy), and V_(zx) measured at a first tool location {right arrow over(r)}₁, and another linear combination of V_(xx), V_(yy), and V_(zx)measured at a second tool location {right arrow over (r)}₂. The form ofthe two linear combinations does not have to be identical. However, forease of discussion, the same linear combination, V_(xx)+V_(yy), is usedbelow. Specifically, two new measurements, attenuation and phase shift,are defined in Equations 5a-5b below:

$\begin{matrix}{{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{{V_{xx}\left( {\overset{->}{r}}_{1} \right)} + {V_{yy}\left( {\overset{->}{r}}_{1} \right)}}{{V_{xx}\left( {\overset{->}{r}}_{2} \right)} + {V_{yy}\left( {\overset{->}{r}}_{2} \right)}} \right)} \right)}}};} & \left( {5a} \right) \\{{{PS} = {{a\; {\tan \left( \frac{{V_{xx}^{i}\left( {\overset{->}{r}}_{2} \right)} + {V_{yy}^{i}\left( {\overset{->}{r}}_{2} \right)}}{{V_{xx}^{r}\left( {\overset{->}{r}}_{2} \right)} + {V_{yy}^{r}\left( {\overset{->}{r}}_{2} \right)}} \right)}} - {a\; {\tan \left( \frac{{V_{xx}^{i}\left( {\overset{->}{r}}_{1} \right)} + {V_{yy}^{i}\left( {\overset{->}{r}}_{1} \right)}}{{V_{xx}^{r}\left( {\overset{->}{r}}_{1} \right)} + {V_{yy}^{r}\left( {\overset{->}{r}}_{1} \right)}} \right)}}}};} & \left( {5b} \right)\end{matrix}$

where the superscripts r and i indicates the real and imaginary parts,respectively. Equations 5a-5b can also be rewritten in terms of the0^(th) harmonic coefficients as shown below in Equations 5a′-5b′:

$\begin{matrix}{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{C_{0}\left( {\overset{->}{r}}_{1} \right)}{C_{0}\left( {\overset{->}{r}}_{2} \right)} \right)} \right)}}} & \left( {5{a'}} \right) \\{{PS} = {{a\; {\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{2} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{2} \right)} \right)}} - {a\; {{\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{1} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{1} \right)} \right)}.}}}} & \left( {5{b'}} \right)\end{matrix}$

More general expressions for i^(th) and j^(th) measurement stations aregiven by:

$\begin{matrix}{{ATT} = {20{\log_{10}\left( {{abs}\left( \frac{C_{0}\left( {\overset{->}{r}}_{i} \right)}{C_{0}\left( {\overset{->}{r}}_{j} \right)} \right)} \right)}}} & \left( {5c} \right) \\{{PS} = {{a\; {\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{j} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{j} \right)} \right)}} - {a\; {{\tan \left( \frac{C_{0}^{i}\left( {\overset{->}{r}}_{i} \right)}{C_{0}^{r}\left( {\overset{->}{r}}_{i} \right)} \right)}.}}}} & \left( {5d} \right)\end{matrix}$

The phase shift and attenuation values defined by the various Equation 5pairs above are not zero so long as the formation properties and/orstructures around {right arrow over (r)}₁ and {right arrow over (r)}₂are different within the depth of investigation. This is true for bothvertical and non-vertical sections. Thus, the measurements are sensitiveto resistivity anisotropy even in vertical wells. As shown in flowchart300 of FIG. 3, a well can be divided into segments such that eachsegment contains at least two measurement positions for which the 0^(th)harmonic coefficients are non-trivially different (step 302). For eachsuch segment, the phase shift and attenuation can be determined based onan Equation 5 pair (step 304). For each segment, the determined phaseshift and attenuation, with or without other measurements, may be usedto invert for resistivity anisotropy and formation structure (step 306),and the result outputted (step 308).

Alternatively, if a vertical section is identified, a neighboringsub-section abutting the vertical section can be identified where thenewly defined measurements of Equations 5a/5b, 5c/5d, or 5a′/5b′ are notzero; that is, where the 0^(th) complex harmonic coefficients arenon-trivially different from station to station within that sub-section.There may be one such sub-section at one end of the identified verticalsection, or there may be one such sub-section at each end of theidentified vertical section. As shown in flowchart 400 of FIG. 4, foreach such neighboring sub-section, the phase shift and attenuation canbe calculated as described above (step 402), and an inversion may beperformed to obtain computed values for the resistivity anisotropy andformation structure (step 404). The theoretical induced voltage for anon-axial transmitter and non-axial receiver pair can be determinedusing the inverted formation parameters and compared to the measuredvoltage to generate one or more gain factors (step 406). The calculatedgain factors are then used to correct the measured voltages for theidentified vertical section (step 408). The corrected voltages may thenbe inverted for anisotropy and formation structure (step 410).

In addition to directional measurements in the non-vertical section(s),non-directional measurements may be obtained and used in the inversioncalculations to obtain resistivity anisotropy and other formationstructure information. For example, if ARC tool-type measurements areavailable, an inversion may be performed to determine horizontalresistivity and bed boundaries. That information can be used with thegain corrected voltages to invert for vertical resistivity. In addition,the theoretical voltages produced from the direct (air) signal may besubtracted from the gain corrected voltages to remove the primary fieldbefore the inversion.

For non-vertical sections, one can use the directional measurementsdefined in Equations 1a and 1b along with other measurements to invertfor the resistivity anisotropy and the formation structure. Thetheoretical voltage for the non-vertical section can be calculated andcompared with the measured voltage to obtain one or more gain factorsfor that non-vertical section. Those gain factors, assuming they arecomparable to the gain factors of a nearby vertical section, can be usedto correct the complex 0^(th) harmonic coefficients of the nearbyvertical section, and the corrected complex 0^(th) harmonic coefficientsof the vertical section can be inverted, with or without othermeasurements, to obtain resistivity anisotropy and formation structureinformation for the vertical section of the wellbore. In a refinement,the induced voltages V({right arrow over (r)}, φ) may be used instead ofthe 0^(th) harmonic coefficients C₀({right arrow over (r)}₁), . . .C₀({right arrow over (r)}_(N)).

The complex 0^(th) harmonic coefficients C₀({right arrow over (r)}₁), .. . C₀({right arrow over (r)}_(N)) from the segments exhibitingsufficient variance amongst C₀({right arrow over (r)}₁), . . . C₀({rightarrow over (r)}_(N)) may be inverted directly to provide gain factors,resistivity anisotropy, and formation structure information for thatsegment. The gain factors are used to correct C₀({right arrow over(r)}₁), . . . C₀({right arrow over (r)}_(N)) for those sections that donot exhibit sufficient variance.

While only certain embodiments have been set forth, alternatives andmodifications will be apparent from the above description to thoseskilled in the art. These and other alternatives are consideredequivalents and within the scope of this disclosure and the appendedclaims.

1. A method to determine formation properties in a substantiallyvertical section of a wellbore, comprising: considering the verticalsection as comprising one or more segments; obtaining measurements witha directional resistivity tool at two or more measurement stationswithin each segment for which the complex 0^(th) harmonic coefficientsfor the obtained measurements are non-trivially different from oneanother; determining, for each such segment, the phase shift andattenuation using the complex 0^(th) harmonic coefficients obtained forthat segment; inverting, for each such segment, for the formationproperties using the determined phase shift and attenuation for thatsegment; and outputting, for each such segment, the formation propertiesdetermined from the inversion for that segment.
 2. The method of claim1, wherein the formation properties include resistivity anisotropy andformation structure.
 3. The method of claim 1, wherein, for one or moreof the one or more segments, but not all of the segments, the complex0^(th) harmonic coefficients for the obtained measurements are onlytrivially different from one another.
 4. The method of claim 3, furthercomprising, for each of the one or more segments for which the complex0^(th) harmonic coefficients for the obtained measurements are onlytrivially different from one another, attributing the formationproperties obtained from one or more of the one or more segments forwhich the complex 0^(th) harmonic coefficients for the obtainedmeasurements are non-trivially different from one another.
 5. The methodof claim 1, wherein the directional resistivity tool has transmitter andreceiver antennas having non-axial dipole moments.
 6. The method ofclaim 1, further comprising using other measurements in addition to thephase shift and attenuation to perform the inversion.
 7. The method ofclaim 6, wherein the other measurements are from transmitter andreceiver antennas having axial dipole moments.
 8. The method of claim 1,wherein each measurement is a logarithmic ratio of a linear combinationof electromagnetic coupling components measured at a first tool locationand another linear combination of electromagnetic coupling componentsmeasured at a second tool location.
 9. The method of claim 8, whereinthe linear combinations are the same.
 10. A method to determineformation properties in a substantially vertical section of a wellbore,comprising: considering the wellbore as comprising one or more firstsegments, for which the complex 0^(th) harmonic coefficients for theobtained measurements are only trivially different from one another, andone or more second segments, for which the complex 0^(th) harmoniccoefficients for the obtained measurements are non-trivially differentfrom one another, abutting each of the first segments; obtainingmeasurements with a directional resistivity tool at two or moremeasurement stations within each second segment; determining, for eachsuch second segment, the phase shift and attenuation using the complex0^(th) harmonic coefficients obtained for that segment; inverting, foreach such second segment, for the formation properties using thedetermined phase shift and attenuation for that segment; determining,for each such second segment, a theoretical induced voltage for anon-axial transmitter and non-axial receiver pair using the invertedformation parameters; comparing, for each such second segment, thedetermined theoretical induced voltage to the measured voltage togenerate one or more gain factors; using the one or more generated gainfactors to correct the measured voltages for each neighboring firstsegment; inverting, for each neighboring first segment, the correctedvoltages for formation properties; and outputting, for each neighboringfirst segment, the formation properties determined from the inversion.11. The method of claim 10, wherein the formation properties includeresistivity anisotropy and formation structure.
 12. The method of claim10, further comprising using other measurements in addition to the phaseshift and attenuation to perform the inversion.
 13. The method of claim12, wherein the other measurements are from transmitter and receiverantennas having axial dipole moments.
 14. The method of claim 10,further comprising using the generated gain factors for the secondsegments located on opposite ends of a particular first segment tocorrect the voltages for that particular first segment.
 15. The methodof claim 10, further comprising subtracting the theoretical voltagesproduced from the direct (air) signal from the gain corrected voltagesto remove the primary field before the inversion.
 16. A method todetermine formation properties in a substantially vertical section of awellbore, comprising: considering the wellbore as comprising one or morefirst segments, for which the complex 0^(th) harmonic coefficients forthe obtained measurements are only trivially different from one another,and one or more second segments, for which the complex 0^(th) harmoniccoefficients for the obtained measurements are non-trivially differentfrom one another, abutting each of the first segments; obtainingmeasurements with a directional resistivity tool at two or moremeasurement stations within each second segment; determining, for eachsuch second segment, the complex 0^(th) harmonic coefficients for thosemeasurements; inverting, for each such second segment, for one or moregain factors and the formation properties using the determined complex0^(th) harmonic coefficients for that segment; using the one or moregenerated gain factors to correct the measured voltages for eachneighboring first segment; inverting, for each neighboring firstsegment, the corrected voltages for anisotropy and formation structure;and outputting, for each neighboring first segment, the formationproperties determined from the inversion.
 17. A system to determineformation properties in a substantially vertical section of a wellborecomprising one or more segments, the system comprising: a directionalresistivity tool to obtain measurements at two or more measurementstations within each second segment for which the complex 0 ^(th)harmonic coefficients for the obtained measurements are non-triviallydifferent from one another; and a processor to: determine, for eachsecond segment, the phase shift and attenuation using the complex 0^(th)harmonic coefficients obtained for that segment; invert, for each secondsegment, for the formation properties using the determined phase shiftand attenuation for that segment; and output, for each second segment,the formation properties determined from the inversion for that segment.18. The system of claim 17, wherein the directional resistivity tool isrun into the wellbore on a wireline, a drill string, or a wired drillpipe.
 19. The system of claim 17, wherein the processor is disposed onor near the directional resistivity tool.
 20. The system of claim 17,wherein the processor further determines one or more gain factors foreach second segment and applies the one or more gain factors to voltagesobtained in a neighboring first segment before inverting those voltagesfor anisotropy and formation structure.
 21. A method to determineformation properties in a substantially vertical section of a wellbore,comprising: considering the wellbore as comprising one or more firstsegments, for which the complex 0^(th) harmonic coefficients for theobtained measurements are only trivially different from one another, andone or more second segments, for which directional measurements can beobtained for each such segment at a particular measurement station,abutting each of the first segments; obtaining measurements with adirectional resistivity tool at one or more measurement stations withineach second segment; determining, for each such second segment, thephase shift and attenuation using the directional measurements obtainedfor that segment at a particular measurement station; inverting, foreach such second segment, for the formation properties using thedetermined phase shift and attenuation for that segment; determining,for each such second segment, a theoretical induced voltage for anon-axial transmitter and non-axial receiver pair using the invertedformation properties; comparing, for each such second segment, thedetermined theoretical induced voltage to the measured voltage togenerate one or more gain factors; using the one or more generated gainfactors to correct the measured voltages for each neighboring firstsegment; inverting, for each neighboring first segment, the correctedvoltages for anisotropy and formation structure; and outputting, foreach neighboring first segment, the formation properties determined fromthe inversion.
 22. The method of claim 21, wherein the formationproperties include resistivity anisotropy and formation structure. 23.The method of claim 21, further comprising using other measurements inaddition to the phase shift and attenuation to perform the inversion.24. The method of claim 23, wherein the other measurements are fromtransmitter and receiver antennas having axial dipole moments.
 25. Themethod of claim 21, further comprising using the generated gain factorsfor the second segments located on opposite ends of a particular firstsegment to correct the voltages for that particular first segment. 26.The method of claim 21, further comprising subtracting the theoreticalvoltages produced from the direct (air) signal from the gain correctedvoltages to remove the primary field before the inversion.